It would behoove you to check the license in order to confirm that whoever gave it to you had the right to do so.
Beyond confirming that you have a legit copy, you don't have to be concerned with the license at all, if you're not redistributing anything.
The vendors of proprietary software and their lawyers dreamed up this idea that a license can lapse based on the user's non-redistributing uses of the work. For instance, if the user reverse-engineers the binary code to understand how it works, then they become unlicensed, the idea then being that they are perpetrating copyright infringement by continuing to have a copy.
The AGPL falls into this category.
The restriction itself does not come from copyright law; copyright law doesn't say things like that allowing network users to interact with a software program is an infringing activity, or that reading the work to understand it is infringing activity.
https://en.wikipedia.org/wiki/Copyright_law_of_the_United_St...
Certainly if you privately modify it is going to be unlikely for someone to find out you did that, but that doesn't make it any less illegal.
You're not breaking the law if you scribble notes in the margin of a textbook; that's just crazy. Even if you pass that on to a friend, for that matter.
Anyway, if a license tries to rely on such draconian doctrines to prevent uses, it's obviously not a free license.
Kind of like how cops in some places in America can evidently arrest someone for DUI if that person merely walks to their car with their car keys, intending to sleep inside until sober.